# Problem 11
#
# In the 20 x 20 grid below, four numbers along a diagonal line
# have been marked in red.
#
# 8 2 22 97 38 15 0 40 0 75 4 5 7 78 52 12 50 77 91 8
# 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 4 56 62 0
# 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 3 49 13 36 65
# 52 70 95 23 4 60 11 42 69 24 68 56 1 32 56 71 37 2 36 91
# 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
# 24 47 32 60 99 3 45 2 44 75 33 53 78 36 84 20 35 17 12 50
# 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
# 67 26 20 68 2 62 12 20 95 63 94 39 63 8 40 91 66 49 94 21
# 24 55 58 5 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
# 21 36 23 9 75 0 76 44 20 45 35 14 0 61 33 97 34 31 33 95
# 78 17 53 28 22 75 31 67 15 94 3 80 4 62 16 14 9 53 56 92
# 16 39 5 42 96 35 31 47 55 58 88 24 0 17 54 24 36 29 85 57
# 86 56 0 48 35 71 89 7 5 44 44 37 44 60 21 58 51 54 17 58
# 19 80 81 68 5 94 47 69 28 73 92 13 86 52 17 77 4 89 55 40
# 4 52 8 83 97 35 99 16 7 97 57 32 16 26 26 79 33 27 98 66
# 88 36 68 87 57 62 20 72 3 46 33 67 46 55 12 32 63 93 53 69
# 4 42 16 73 38 25 39 11 24 94 72 18 8 46 29 32 40 62 76 36
# 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 4 36 16
# 20 73 35 29 78 31 90 1 74 31 49 71 48 86 81 16 23 57 5 54
# 1 70 54 71 83 51 54 69 16 92 33 48 61 43 52 1 89 19 67 48
#
# The product of these numbers is 26*63*78*14 = 1788696.
#
# What is the greatest product of four adjacent numbers 
# in any direction (up, down, left, right, or diagonally)
# in the 20x20 grid?

a = []
a.append([8,2,22,97,38,15,0,40,0,75,4,5,7,78,52,12,50,77,91,8])
a.append([49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,4,56,62,0])
a.append([81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,3,49,13,36,65])
a.append([52,70,95,23,4,60,11,42,69,24,68,56,1,32,56,71,37,2,36,91])
a.append([22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80])
a.append([24,47,32,60,99,3,45,2,44,75,33,53,78,36,84,20,35,17,12,50])
a.append([32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70])
a.append([67,26,20,68,2,62,12,20,95,63,94,39,63,8,40,91,66,49,94,21])
a.append([24,55,58,5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72])
a.append([21,36,23,9,75,0,76,44,20,45,35,14,0,61,33,97,34,31,33,95])
a.append([78,17,53,28,22,75,31,67,15,94,3,80,4,62,16,14,9,53,56,92])
a.append([16,39,5,42,96,35,31,47,55,58,88,24,0,17,54,24,36,29,85,57])
a.append([86,56,0,48,35,71,89,7,5,44,44,37,44,60,21,58,51,54,17,58])
a.append([19,80,81,68,5,94,47,69,28,73,92,13,86,52,17,77,4,89,55,40])
a.append([4,52,8,83,97,35,99,16,7,97,57,32,16,26,26,79,33,27,98,66])
a.append([88,36,68,87,57,62,20,72,3,46,33,67,46,55,12,32,63,93,53,69])
a.append([4,42,16,73,38,25,39,11,24,94,72,18,8,46,29,32,40,62,76,36])
a.append([20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,4,36,16])
a.append([20,73,35,29,78,31,90,1,74,31,49,71,48,86,81,16,23,57,5,54])
a.append([1,70,54,71,83,51,54,69,16,92,33,48,61,43,52,1,89,19,67,48])

l = []
# Go from left to right 
for r in range(0,len(a)):
    for c in range(0,17):
        l.append(a[r][c:c+4])

# now do from top to bottom
for c in range(0,len(a)):
    for r in range(0,17):
        l.append( [a[r][c], a[r+1][c], a[r+2][c], a[r+3][c]] )

# next do for horizontals running upper-left down lower-right        
for r in range(0, 17):
    for c in range(0,17):
        l.append( [ a[r][c], a[r+1][c+1], a[r+2][c+2], a[r+3][c+3] ] ) 

# last, do for horizontals running in the reverse
for r in range(0,17):
    for c in range(3,len(a)):
        l.append( [ a[r][c], a[r+1][c-1], a[r+2][c-2], a[r+3][c-3] ] )

answer = map(lambda e:e[0]*e[1]*e[2]*e[3], l)

print "-> ", max(answer)
